- Obvious recommendation is obvious: The Beatles. Everyone who isn't Helen Keller knows about them and has heard something by them. My favorite album is Let It Be, although they're ALL amazing. You can't go wrong here. (Similar bands: Rolling Stones, Simon and Garfunkel)
- Eels. Not many people recognize the name of this band, but chances are you've heard them before. Or rather, "him". Eels only has one constant band member, Mark Oliver Everett, usually called "E". E writes the songs and is usually the main vocal. He has an amazing range, and his lyrics are always powerful and heartfelt. And his voice is kind of gravelly and badass. BONUS- they just came out with a new album! www.youtube.com/watch (similar bands: Bob Dylan, The Beatles)
- They Might Be Giants. They have been reliably pushing out awesome songs since the early 80s, including a wide variety of quirky songs for their usual audience and a growing collection of children's songs that are entertaining no matter how old you may be. Their subject matter ranges from the mundane to the downright weird (for example, Piece of Dirt and Purple Toupee). www.youtube.com/watch (similar bands: Scissor Sisters, Weezer, Adam Ant)
- Guster. This band pairs gorgeous folk guitar lines with some of the most creative (often bongo-centric) rhythms I've ever heard. Their lyrics are always intricate and beautiful, as well. www.youtube.com/watch (similar bands: Iron and Wine, Harry Chapin, Barenaked Ladies)
- Rufus Wainwright. His lyrics are sometimes hilarious, sometimes incredibly sentimental, but are never dull. His voice is angelic, and his skill on piano is unmatched. http://www.youtube.com/watch?v=mmbQEQltOwM (Similar bands: Ingrid Michaelson, Sara Bareilles)
There are so many, but... yeah.